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Geometry and Analysis - Theory, History and Applications 

The main research interests of this group are Analysis, Dynamical Systems and their interdisciplinary applications, Differential Geometry, Algebraic Topology, History and Epistemology of Mathematics. Among the members of the group, there are six doctoral students. Senior members of the group are currently supervising Master, Doctoral and Postdoctoral research.

Analysis
  • Global asymptotic stability of an equilibrium point of a n-dimensional system of delay differential equations
  • Asymptotic expansion in qualitative theory of differential equations. 
  • Existence, regularity and asymptotic behavior of solutions of nonlinear evolutive systems of equations or variational and quasivariational inequalities involving operators of type p- Laplacian or p-Rot.

Dynamical Systems
  • Spectral stability of semigroups of stochastic dynamical systems
  • Quantization of disordered dynamical systems
  • Geometry of infinitely renormalizable Henon maps
  • Theory of pseudo- diffeomorphisms in Cr new flat structures
  • Fine Structures of Hyperbolic Diffeomorphisms (already accepted to be a Springer Monograph)
  • Links between dynamical systems and hydrodynamic limit theory for particles
  • Interdisciplinary applications to epidemiology, neurology, immunology, financial mathematics and industrial organization
  • Production of  interactive material for general public and schools in dynamical systems and applied mathematics.
Differential Geometry and Algebraic Topology
  • Quaternionic Kähler manifolds (Project with IST and the University of Évora)
  •  Generalized and Riemannian Geometry aiming to classify metric connections with totally skew-symmetric torsion which have vanishing Riemann/Ricci tensor.
  • Homotopy Theory: H-spaces, homotopy and homology of manifolds, numerical homotopy invariants and rational homotopy theory
  • Computational Algebraic Topology and applications to Dynamical Systems
  • Applications of Algebraic Topology in other research areas such as Robotics or Concurrency Theory
History and Epistemology of Mathematics
  • 18th century European Mathematics (Analysis and Geometry) and on the reform conducted, at that time, on the Portuguese educational system. Research work conducted during the past two years with colleagues from the Departments of Mathematics of Porto, Coimbra and Lisboa will also be pursued.
  • 18th-century European mathematics, and its reception in Portugal


 
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